According to the newspaper, Carolina Panthers defensive coordinator Steve Wilks did get past the first round of interviews. The report also said former Denver Broncos running backs coach Eric Studesville and Steve Spagnuolo, who finished the season as the team's interim coach are not being considered for the position.
All three remaining candidates are currently preparing for playoff games and are linked to other openings.
Shurmur, who is the Minnesota Vikings offensive coordinator, is considered a candidate for the Arizona Cardinals opening. McDaniels, who is the offensive coordinator for the New England Patriots, also may be a candidate for the Indianapolis Colts.
Patricia, who is New England's defensive coordinator, also has been connected to the Detroit Lions opening.
On Thursday, Patricia was considered the favorite for the job. The New York Daily News reported Wednesday all signs pointed towards New England's defensive coordinator as emerging as the first coaching hire under new GM Dave Gettleman.
Complicating matters for the Giants is since all three are currently in the postseason, the team cannot meet with them due to the league's tampering rules. The rule states: "No contract shall be executed, and no agreement to execute a contract, or an announcement of a contract or of an agreement for employment, shall be permitted until after the conclusion of the employer club's playing season."
The rule, however can be circumvented by the Giants reaching an unofficial agreement in the next few days.
Last year, the San Francisco 49ers hired Kyle Shanahan while he was still serving at the offensive coordinator for the Atlanta Falcons in their run to the Super Bowl. Three years ago, Dan Quinn was hired as Atlanta's head coach while he was the Seattle Seahawks defensive coordinator.
Giants co-owner John Mara previously stated he wanted someone with head coaching experience or a long-time head coach.
McDaniels was 11-17 in parts of two seasons with the Denver Broncos in 2009 and 2010. He went 8-8 in his first season and was fired after going 3-9 in 2010.
Patricia has been an assistant with the Patriots since 2004 and the team's defensive coordinator since the 2012 season.